Product Market Performance and Capital Structure : A Hierarchical Bayesian Semi-Parametric Panel Regression Model

This paper proposes a parsimonious model to investigate the conjecture of non monotonous relation between a firm's product market performance and its capital structure with special reference to emerging economy. A semi-parametric model has been proposed here to understand the non-linearity induced by the non-monotonicity conjecture. Since the nature of market and its dynamics may differ over economies, we propose to partition the range of the proxy of capital structure in low, medium and high sub-intervals and use piecewise linear curve or spline therein to account for the non-linearity. We use in this paper hierarchical Bayesian adaptive spline to estimate the ranges of the sub-intervals along with the slopes of the line segments after controlling for other financial factors. In turn, the adaptive spline paves the way for comparison between economies in terms of product market responsiveness to the capital structure of firms. The inconsistency in parameter estimation caused by endogeneity, multi-collinearity and heteroscedasticity together is addressed here parsimoniously by postulating optimization of penalized squared error loss in Ridge estimation as a Bayesian optimization problem and selecting priors with suitable hyper parameters